with the \(\left( \pm \right) \)  sign for Dirichlet and Neumann boundary
condition, respectively. Again, in the case of the \(x\) -orientation the Casimir
energy goes to zero, as for the Schwarzschild geometry when the orbital motion
of the cavity approaches a null geodesic orbit at \(r=3M\)  [1]}. But, in
the \(y\) -orientation, the energy diverges for a value with a sign opposite
\(\mathcal {E}_{m}\) . The Casimir force (energy) disappear at the angular
velocity
\(\Omega =\Omega _{0\pm }=\omega _{d}\pm \sqrt{\frac{\Delta }{3}}\frac{r^{2}}{A}\Longrightarrow \bar{\epsilon }_{vac}^{\left( y\right) }=0~. \) 
<FIGURE>